Astronomical Systems

This table lists nearly a hundred astronomical systems from the Han period to the end of imperial China. It omits half a dozen early schemata (items 1-6 in CTK) that generate only simple lunisolar calendars, and about which little is known. Item 1 is a version of one of these, important because item 4, a complete system, was based on it, and item 2 was explicitly meant to reform it. On the "old" Warring States calendars see Chen 2003: 87-92.

This is far from a complete list. Of the roughly 200 systems of which there is some record, I include only those about which we have some basic information. Almost all occur in three sources, the Season-granting system (SGS); Ch弾n Mei-tung 1995: 215-23, table 8-1 (CMT); and Ch弾n Tsun-kuei 1980-84: III, 1399-1407, table 50 (CTK). I have also consulted Yabuuti 1963, which lists additional systems about which there is very little reliable information.

The Title column contains only those from SGS. Titles in the form "nth year" refer to the sexagenary year number of the epoch. The dynasty column uses the abbreviations F. (former, ch段en ), L. (latter, hou ), N. (northern, pei ), E. (eastern, tung ), S. (southern, nan ), and W. (western, hsi 西). In the last column, inclusive dates are those of official use as given in SGS. Single dates mark either systems that did not achieve official status or official systems not recognized by SGS. A number of the dates in SGS are incorrect; see my notes. Those in CTK are also often inexact. Many of the dates require further study; I have added in square brackets the terminal dates of official status when known. In the "dynasty" column I add a plus sign when a system remained official past the end of a dynasty. Although I normally list only the person customarily credited with authorship, most systems were the products of collaboration.

No.

SGS

CMT

CTK

Dynasty

Title

Title in CMT or CTK

Author

Dates

1

 

1

 

F. Han

 

Quarter-Day (Ssu fen li 四分暦)

Anonymous

Unknown

2

 

2

7

F. Han

Grand Inception (T誕i ch置 太初)

 

Teng P段ng 鄧平

104 B.C-A.D.1/5

3

1

 

8

F. Han+

Triple Concordance (San t置ng li 三統暦)

 

[Liu Hsin 劉歆]

A.D. 1/5-85 (note 1)

4

2

3

9

L. Han

Quarter-Day (Ssu fen li 四分暦)

Later Han Quarter-Day ([Hou Han] Ssu fen li [後漢] 四分暦)

Pien Hsin 編訢

85-206

5

3

4

10

L. Han+

Supernal Emblem (Ch段en hsiang li 乾象暦)

 

Liu Hung 劉洪

206-37

6

 

5

11

Wei

 

Yellow Inception (Huang ch置 li 黃初暦)

Han I 韓翊

220

7

 

6

12

Wei

 

Grand Harmony (T誕i ho li 太和暦)

Kao T誕ng-lung 高堂隆

227

8

4

7

13

Wei+

Luminous Inception (Ching ch置 li 景初暦)

 

Yang Wei 楊偉

237-443

9

 

 

16

Tsin

 

Supernal Standard (Ch段en tu li 乾度暦)

Li Hsiu 李修

c. 277

10

 

8

17

Tsin+

 

Perpetual Harmony (Yung ho li 永和暦)

Wang Shuo-chih 王朔之

352

11

 

 

15

Tsin

 

Correct (Cheng li 正暦)

Liu Chih劉智

c. 352

12

 

9

14, 20

Tsin

 

Grand Beginning (T誕i shih li 泰始暦)

Liu Chih

365

13

 

10

18

L. Ch段n

 

Triple Era 1st-year

Epoch (San chi chia-tzu yuan li 三紀甲子元暦)

Chiang Chi 姜岌

384[-417]

14

 

11

19

N. Liang+

 

Epochal Beginning (Hsuan shih li 玄始暦)

Chao Fei {+ r. side of }

c. 412[-522] (note 2)

15

 

 

22

Sung

 

Seven Luminaries Past (Chi wang ch段 yao li 既往七曜暦)

Hsu Kuang 徐廣

c. 424

16

 

 

21

N. Wei

 

Triple Spreading Epoch (San hsuan yuan li 三宣元暦)

Ts置i Hao 崔浩

c. 440

17

5

12

23, 24

Sung+

Epochal Excellence (Yuan chia li 元嘉暦)

 

Ho Ch弾ng-t段en 何承天

443-63 (note 3)

18

6

13

25

Sung

Great Enlightenment (Ta ming li 大明暦)

 

Tsu Ch置ng-chih 祖沖之

463-521 (note 4)

19

 

 

26

N. Wei

 

Luminous Enlightenment (Ching ming li 景明暦)

Kung-sun Ch置ng 公孫崇

507

20

 

 

27

N. Wei

 

Divine Tortoise (Shen kuei li 神龜暦)

Ts置i Kuang 崔光

518? (note 5)

21

7

14

28

N. Wei

Orthodox Glory (Cheng kuang li 正光暦)

 

Chang Lung-hsiang 張龍祥

518-40

22

 

 

33

N. Ch段

 

Numinous Pattern (Ling hsien li 靈憲暦)

Hsin-tu Fang 信都芳

by 539? (note 6)

23

8

15

29

E. Wei

Ascendant Harmony (Hsing ho li 興和暦)

 

Li Yeh-hsing 李業興

540-50

24

 

16

30

Liang

 

Great Unity (Ta t置ng li 大同暦)

Yü K置o

544

25

 

17

31

E. Wei

 

Nine-grid Chess (Chiu kung hsing ch段 li 九宮行棋暦)

Li Yeh-hsing

547 (note 7)

26

9

18

32

N. Ch段

Celestial Preservation (T段en pao li 天保暦)

 

Sung Ching-yeh 宋景業

550-66 (note 8)

27

 

 

 

N. Chou

 

Chou (Chou li 周暦? )

Ming K弛-jang 明克讓

559? (note 9)

28

10

19

34

N. Chou

Celestial Harmony (T段en ho li天和暦)

 

Chen Luan 甄鸞

566-79

29

 

20

35

N. Ch段

 

Martial Tranquillity (Wu p段ng li 武平暦)

Liu Hsiao-sun 劉孝孫

576

30

 

21

36

N. Ch段

 

50th-year Epoch (Chia-yin yuan li 甲寅元暦)

Tung Chün 董峻

576

31

 

22

37

N. Ch段

 

Meng-pin (Meng-pin li 孟賓暦)

Chang Meng-pin 張孟賓

576

32

11

23

38

N. Chou+

Great Emblem (Ta hsiang li大象暦)

 

Ma Hsien 馬顯

579-84

33

12

24

39

Sui

Opening Sovereignty (K誕i huang li開皇暦)

 

Chang Pin 張賓

584-608 (note 10)

34

42

25

40

Sui+

Sovereign Pole (Huang-chi li 皇極曆)

 

Liu Cho 劉焯

608

35

13

26

41

Sui

Great Patrimony (Ta yeh li大業暦)

 

Chang Chou-hsuan 張胄玄

608-19

36

14

27

42

T誕ng

15th-Year (Wu-yin li 戊寅曆)

 

Fu Jen-chün傅仁均

619-65

37

 

 

45

T誕ng

 

Warp and Weft (Ching-wei li 經緯暦)

Chü-t誕n Lo 瞿曇羅

by 664 (note 11)

38

15

29

44

T誕ng

Chimera Virtue (Lin-te li麟德暦)

 

Li Ch置n-feng 李淳風

665-728

39

 

 

46

T誕ng

 

Shining Residence (Kuang chai li 光宅暦)

Chü-t誕n Lo

(Indian)

698

40

 

30

47

T誕ng

 

Divine Dragon (Shen lung li 神龍暦)

Nan-kung Yueh 南宮說

705

41

 

28

48

T誕ng

 

Nine Upholders (Chiu-chih li 九執暦)

Anonymous [Indian]

718 (note 12)

42

16

31

49

T誕ng

Great Expansion (Ta-yen li 大衍暦

 

I-hsing 一行

728-62 (note 13)

43

 

 

50

T誕ng

 

Thousand Year (Ch段en sui li 千歲暦)

Wang Po 王勃

8th cent.

44

 

 

51

T誕ng

 

Seven Luminaries (Ch段 yao li 七曜暦)

Wu Po-shan 吳伯善

8th cent.

45

17

32

53

T誕ng

Fivefold Era (Wu chi li 五紀暦)

 

Kuo Hsien-chih 郭獻之

752-85 (note 14)

46

 

 

52

T誕ng

 

Perfect Virtue (Chih te li 至德暦)

Han Ying 韓穎

758[-62]

47

 

 

43

T誕ng

 

Tallying with Heaven (Fu t段en li 符天暦)

Ts誕o Shih-wei 曹士蒍

780/83 (note 15)

48

18

33

54

T誕ng

Constant Epoch (Chen yuan li貞元暦)

Constant Epoch (Cheng-yuan li 正元暦)

Hsu Ch'eng-ssu 徐承嗣

785-822 (note 16)

49

 

 

55

T誕ng

 

Phenomenal Contemplation (Kuan hsiang li 觀象暦)

Hsu Ang 徐昂

807[-22] (note 17)

50

19

34

56

T誕ng

Extending Enlightenment (Hsuan ming li 宣明暦)

 

Hsu Ang

822-93 (note 18)

51

20

35

57

T誕ng+

Reverence for the Arcana (Ch置ng hsuan li 崇玄暦

 

Pien Kang 邊岡

893-956 (note 19)

52

 

 

59

F. Shu

 

Eternal Glory (Yung ch誕ng li 永昌暦)

Hu Hsiu-lin 胡秀林

ca. 911?

53

 

 

60

F. Shu?

 

Correct Phenomena (Cheng hsiang li 正象暦)

 

after 911? (note 20)

54

 

 

58

5 Dyn.

 

Myriad Parts (Wan fen li 萬分暦)

Anonymous, popular

ca. 920?

55

 

 

61

L. Tsin

 

Adjusted Epoch (T段ao yuan li 調元暦)

Ma Ch置ng-chi 馬重績

938

56

 

 

62

S. T誕ng

 

Centered and Upright (Zhong-zheng li 中正暦)

Ch弾n Ch弾ng-hsun 陳成勛

940

57

 

 

63

S. T誕ng

 

Orderly Governance (Ch段 cheng li 齊政暦)

Unknown

940/75

58

 

 

64

L. Chou

 

Resplendent Arcana (Ming yuan li 明玄暦)

Wang Ch'u-no王處訥

956

59

21

36

65

L. Chou+

Veneration for Heaven (Ch段n t段en li 欽天暦)

 

Wang P'u 王朴

956-60 (note 21)

60

22

37

66

Sung

Response to Heaven (Ying t段en li 應天暦)

 

Wang Ch'u-no

960-81

61

23

38

67

Sung

Supernal Epoch (Ch段en yuan li 乾元暦)

 

Wu Chao-su 吳昭素

981-1001

62

 

 

77

Liao

 

Great Enlightenment

Chia Chün 賈俊

994[-1126] (note 22)

63

 

39

68

Sung

 

Perfect Way (Chih tao li 至道理)

Wang Jui 王睿

995 (note 23)

64

24

40

69

Sung

Matching Heaven (I t段en li 儀天暦)

 

Shih Hsu 史序

1001-24

65

 

41

70

Sung

 

Supernal Ascendance (Ch段en hsing li 乾興暦)

Chang K置ei 張奎

1022

66

25

42

71

Sung

Reverence for Heaven (Ch置ng t段en li 崇天暦)

 

Sung Hsing-ku 宋行古

1024-64

67

26

43

72

Sung

Resplendent Heaven (Ming t段en li 明天暦)

 

Chou Ts置ng 周琮

1064-74

68

27

44

73

Sung

Oblatory Epoch (Feng yuan li 奉元暦)

 

Wei P'u 衛朴

1074-92 (note 24)

69

28

45

74

Sung

Contemplation of Heaven (Kuan t段en li 觀天暦)

 

Huang Chü-ch'ing 皇居卿

1092-1103 (note 25)

70

29

46

75

Sung

Augury of Heaven (Chan t段en li 占天暦)

 

Yao Shun-fu 姚舜輔

1103-6

71

30

47

76

Sung

Era Epoch (Chi yuan li 紀元暦)

 

Yao Shun-fu

1106-27

72

31

48

78

Chin

Great Enlightenment

 

Yang Chi 楊級

1127-80

73

33

49

79

Sung

Concordant Epoch (T置ng yuan li 統元暦)

 

Ch'en Te-i 陳得一

1135-67)

74

34

50

80

Sung

Supernal Way (Ch段en tao li 乾道暦)

 

Liu Hsiao-jung 劉孝榮

1167-76 (note 26)

75

35

51

81

Sung

Splendor through Simplicity (Ch置n hsi li淳熙暦)

 

Liu Hsiao-jung

1176-91

76

32

53

82

Chin

Revised Great Enlightenment (Ch置ng hsiu Ta ming li 重修大明暦)

 

Chao Chih-wei 趙知微

1180-1281 (note 27)

77

43

52

83

Jin

Thirty-second Year (I wei li 乙未暦)

 

Yeh-lü Lü 耶律履

c. 1180

78

 

54

84

Sung

 

Repeated Five-star Conjunction (Wu-hsing tsai chü li 五行再聚暦)

Shih Wan 石萬

1187

79

36

55

85

Sung

Coincident Epoch (Hui yuan li 會元暦)

 

Liu Hsiao-jung

1191-99

80

37

56

86

Sung

Concord with Heaven (T置ng t段en li 統天暦)

 

Yang Chung-fu 楊忠輔

1199-1207

81

38

57

87

Sung

Spreading Joy (K誕i hsi li開禧暦)

 

Pao Huan-chih 鮑澣之

1207-51

82

 

58

88

Yuan

 

Western Expedition 7th-year Epoch (Hsi cheng keng-wu yuan li 西征庚午元暦)

Yeh-lü Ch置-ts誕i 耶律楚材

c. 1221 (note 28)

83

39

59

89

Sung

Protection through Simplicity (Ch置n yu li淳祐暦)

 

Li Te-ch'ing 李德卿

1250-52 (note 29)

84

40

60

90

Sung

Coincidence with Heaven (Hui t段en li 會天暦)

 

T'an Yü 譚玉

1253-71

85

 

 

91

Yuan

 

Myriad Year (Wan nien li 萬年暦)

Jamāl al-Dīn (Persian)

1267

86

41

61

92

Sung

Attainment of Heaven (Ch弾ng t段en li 成天暦

 

Ch'en Ting 陳鼎

1271-76

87

 

 

93

Sung

 

Founded in Heaven (Pen t段en li 本天暦)

Teng Kuang-chien 鄧廣薦

1276 (note 30)

88

44

62

94

Yuan

Season-Granting system (Shou shih li 授時暦)

 

Kuo Shou-ching 郭守敬

1281[-1384]

89

 

63

95

Ming

Muslim (Hui-hui li 回回暦)

 

Wu Po-tsung 吳伯宗

1382

90

 

64

96

Ming

 

Great Concordance 大統

Liu Chi 劉基

1384[-1644] (note 31)

91

 

65

97

Ming

 

Sagely Longevity Myriad Year (Sheng shou wan nien li 聖壽萬年暦)

Chu Tsai-yü 朱載堉

c. 1590? (note 32)

92

 

66

98

Ming

 

Yellow Bell (Huang chung li 黃鍾暦)

Chu Tsai-yü

by 1581

93-94

 

67-68

 

Ming

 

Titles unknown

Hsing Yun-lu 邢雲路

c. 1610 (note 33)

95

 

70

99

Ming

 

New Method (Hsin fa li 新法暦)

Hsu Kuang-ch段 徐光啟

1628

96

 

71

101

Ch段ng

 

Temporal Pattern (Shih hsien li 時憲暦)

J. A. Schall v. Bell

1644[-1742]

97

 

69

100

Ch段ng

 

Hsiao-an (Hsiao-an li 曉庵暦)

Wang Hsi-shan 王錫闡

c. 1656 (n. 34)

98

 

72

102

Ch段ng

 

40th-year (Kuei-mao li 癸卯暦)

Ignatius Kögler

1742[-1644]

 

Notes

1. So far as we now understand it , the Grand Inception system of Pien Hsin et al. was a set of basic lunisolar procedures that Liu Hsin , ca. A.D. 1-5 , extended to include what became the standard contents of astronomical systems. See Sivin 1995a , chap. 2 , p. 11.

2. CMT 255 gives the title as Yuan shih li 元始暦. Early sources differ about the correct title of the regnal era for which the system is named. The difference is almost certainly due to a historical taboo, but Ch弾n Yuan 1928 does not list a pertinent one.

3. When continued in use under the Ch段 dynasty, this system was renamed Established Epoch (Chien yuan 建元).

4. This outstanding system, because it was attacked by a court favorite, was not adopted in the Sung period, but it was used under the Liang and Ch弾n dynasties. The dates of official use should be 510-89. See Sung shu, 13: 304-17.

5. Although Ts置i proposed a system with this title, it was renamed Orthodox Glory when enacted in 518 (apparently not 521), although the source is slightly ambiguous. Li Yeh-hsing was the astronomer most prominently involved. See Wei shu, 107A: 2662-63.

6. This date is quite uncertain; see the discussion in Ch弾n Mei-tung 2003: 294.

7. CMT gives the title as Chiu kung li 九宮暦, and CTK as Chiu kung hsing ta li 九宮行答暦. Chen Mei-tung corrects the error in 2003: 288-89.

8. The terminal date of use depends on when one ends the N. Ch段 dynasty. Although conservative historians end it in 557, with the beginning of the N. Chou period, the last year of its last ruler was 577. The year 566 is significant only as the date of the N. Chou痴 second calendar reform (the first was very obscure), but this made it attractive to compilers seeking a hapless sequence.

9. See Yabuuti 1964: 455, item 12, and Ch弾n Mei-tung 2003: 304-5.

10. The transition from this item to item 34 was actually in 609; see Sui shu, 17: 435.

11. On the dates of this and the next item, see Ch弾n Mei-tung 2003: 357.

12. This is probably when this treatise was translated from Sanskrit or another Indian language. When it was compiled remains unknown (Ch弾n 2003: 359). Yabuuti 1979 is a translation and study.

13. This system was replaced by the Perfect Virtue system in 758; see Hsin T誕ng shu, 27B: 635.

14. This system was actually adopted in 763. See Hsin T誕ng shu, 29: 695.

15. CTK lists only the epoch of this popular system (660), but it was compiled more than a century later; see Momo Hiroyuki 1964.

16. This system was official from 783 to 806. See Ch弾n Mei-tung 2003: 401. The difference between the titles given in the Yuan system and by the two modern sources is due to a taboo on the personal name of the third Sung emperor (Ch弾n Yuan 1928: 154).

17. See Hsin T誕ng shu, 30A: 739.

18. This system was adopted in Korea from the early 9th century to 1392, and in Japan from 861 to 1684. In both countries the Season-granting system succeeded it; Ch弾n Mei-tung 2003: 407.

19. CTK gives the title as Ch置ng yuan li 崇元暦, another instance of taboo avoidance.

20. CTK gives the epoch of this item as "Hou Shu Yen-k誕ng yuan-nien後蜀延康元年," and that of the last as "Hou Shu Yung-p段ng yuan-nien," but basic reference works (e.g., Ku Ching 1995: 60, Li Ch置ng-chih 1981: 133) list the date of the latter as in Former Shu, and give no such reign as the former in the Five Dynasties. See also Ch弾n Mei-tung 2003: 419.

21. Actually used until 963, when the Response to Heaven system superseded it. See Sung shih, 68: 1498.

22. For the dates, see Ch弾n Mei-tung 2003: 491.

23. CTK unaccountably dates items 63-71 (its items 68-76) as Later Chou, but that dynasty ended in 960.

24. Actually used 1075-94, when the Contemplation of Heaven system replaced it; Yü hai, 10: 32a-33b.

25. Some early sources give the author痴 name as Huang Chü-ch'ing 黃居卿; see Ch弾n Mei-tung 2003: 485.

26. The transition from this item to the Splendor through Simplicity system came in 1177; Yü hai, 10: 35a-40b.

27. The Season-granting system lists this item out of chronological order, no doubt because it is a revision of item 72.

28. This pre-dynastic Yuan system is often cited (here by CMT) simply as Keng-wu yuan li. It survives in Yuan shih, ch. 57-58.

29. See my note to the Evaluation, s.v., for the correct dates, 1252-53.

30. For the date, see Yuan shih, 82: 1953.

31. Liu drafted this system in 1355, but it was not used until the Ming period; Ming shih, 31: 516-17.

32. On the dates of this and the next item, see the discussion in Ch弾n Mei-tung 2003: 612.

33. CTK devotes its items 67-68 to lost treatises by Hsing Yun-lu. The excerpts in Ku chin lü li k誕o indicate that both are revisions of SGS. Of the remaining items in this table, 96 and the revision of it in 98 are treatises in the conventional mode. It is uncertain whether 95 and 97 were astronomical systems.

34. On this item see Sivin & Fang 1976: 1379-80.

Sources

CMT: Ch弾n Mei-tung 陈美东. 1995. Ku li hsin t誕n 古历新探 (New investigations of ancient astronomy). Shenyang: Liao-ning chiao-yü CPS. Essays from the 1980痴, which make up a systematic topical history of computational techniques and their evolving accuracy.

CTK: Ch弾n Tsun-kuei . 1980-84. Chung-kuo t段en-wen-hsueh shih (History of Chinese astronomy). 3 vols. Shang-hai: Shang-hai Jen-min Ch'u-pan-she.

SGS: Shou-shih li 授時暦 (Season-Granting system). In Yuan shih 元史, "Li chih 暦志" (Treatise on mathematical astronomy, History of the Yuan dynasty), ch. 52-55.

Ch弾n Mei-tung 陈美东. 2003. Chung-kuo k弛-hsueh chi-shu shih. T段en-wen-hsueh chüan 中国科学技术史。 天文学卷 (History of Chinese science and technology. Astronomy). Beijing: K弛-hsueh Ch置-pan-she. Chronological and topical, much of it arranged by system. Covers to 1911. Indices of authors and writings.

Momo Hiroyuki 桃裕行. 1964. Futenreki ni tsuite 符天暦について (On the Tallying with Heaven astronomical system). Kagakushi kenkyū 科学史研究, 71: 118-19.

Sivin, Nathan. 1969. Cosmos and Computation in Early Chinese Mathematical Astronomy. Leiden: E. J. Brill. Reprinted in Sivin 1995a as chap. 2.

Sivin, Nathan; Fang Chaoying. 1976. Wang Hsi-shan. In Dictionary of Ming Biography. 1368-1644, ed. L. Carrington Goodrich, II, 1379-82. New York: Columbia University Press.

Sivin, Nathan. 1995a. Science in Ancient China. Researches and Reflections. Variorum Collected Studies Series. Aldershot, Hants: Variorum.

Ku chin lü li k誕o 古今律暦考 (Studies of mathematical harmonics and astronomy, ancient and modern). Hsing Yun-lu 邢雲路. 1607. In Pai pu ts置ng-shu chi-ch弾ng 百部叢書集成.

Yü hai 玉海 (Ocean of jade [encyclopedia]). By Wang Ying-lin 王應麟. 1267?. Ed. of 1352, reprint, Taipei: Ta Hua Shu-chü, 1977.

 



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